The Easiest Number Theory Problem

Number Theory Level 1

Let $A$ be set of all prime numbers, and let $B$ be set of all even numbers. Find the number of terms in the set $A \cap B$ .

The answer is 1.

7 solutions

Math Man
Sep 23, 2014

the only even prime number is 2 , thus , n(A U B) = 1

I put zero cuz my brain crashed thinking that no evens were primes, forgetting about 2

Trevor Arashiro - 6 years, 8 months ago

lol , be more careful my freind :)

math man - 6 years, 8 months ago

here it should be n(A intersection B) then the answer comes as 1 your question means a union b that is number of all elements that are prime numbers as well as even numbers n(A U B) means number of all elements in set A and B

U Z - 6 years, 8 months ago

It took me a moment to realize that $n(S)$ where $S$ is some set is equivalent to $|S|,$ the cardinality of the set.

Trevor B. - 6 years, 8 months ago

$2$ is the only even prime because $2$ divides all other even numbers, and they are called even numbers because $2$ divides them.

Satvik Golechha - 6 years, 8 months ago

@megh choksi has a good point. I edited the problem so please make sure that the meaning has not changed.

Trevor Arashiro - 6 years, 8 months ago

ok thank you @Trevor Arashiro

math man - 6 years, 8 months ago

yay 100 solvers

math man - 6 years, 8 months ago

why the answer is 1? 1 isn't even number.....

Billy Lorenzo - 6 years, 8 months ago

it asks the number of the even primes

math man - 6 years, 8 months ago

1 is not prime number and it is not even number ..... how to be the result of intersection between the sets

Randa El-Gabry - 6 years, 8 months ago

the union of the sets will be all natural numbers

Randa El-Gabry - 6 years, 8 months ago

please send me a reply

Randa El-Gabry - 6 years, 8 months ago

how i can forget about 2 .... give me steps for answer

Randa El-Gabry - 6 years, 8 months ago

but 1 is not even and is not prime ........ please answer me

Randa El-Gabry - 6 years, 8 months ago

I can't understand how AUB= 1 I think the answer is all the prime numbers and all the even numbers where the answer will be natural numbers from 0,1,2........................... which is infinite set

Randa El-Gabry - 6 years, 8 months ago

Jitendra Prajapati
Oct 1, 2014

A consists all prime no. i.e. 2, 3, 5, 7 and B consists of all even no. and only no. 2 is both even and prime Hence no. of element in set is 1.

Exactly. People are forgetting that the answer is 1 because 2 occupies the 1st spot in both sets. The intersection is 2 but the answer is 1.

Michael Bartholic - 6 years, 7 months ago

Eddie Pedemont
Oct 13, 2015

Because this is using an intersection of two sets, instead of a union, you can only have the numbers that appear in both sets in the final set. Because 2 is the only prime number, the number of items in the intersection of both sets is one.

Sunitha Bhadragiri
Nov 24, 2014

Write a solution.2 is the only prime even therefore 1

Sandeep Kumar
Oct 5, 2014

2 is only one digit which is prime number as well as even no.

Nayyar Tanoli
Sep 30, 2014

the only common number in even and prime is 2 so number is 1

thanks I get it

Randa El-Gabry - 6 years, 8 months ago

its easy for mathmation

Nayyar Tanoli - 6 years, 8 months ago

what is that

math man - 6 years, 8 months ago

Manoj Kiran
Sep 26, 2014

1 A={x:x is a prime number, x belongs to N} B={x:x is an even number, x belongs to N}(or)B={2, 4, 6, 8, ...} The common number for the sets A and B is an EVEN PRIME NUMBER. The only even prime number in the natural numbers is 2. So A intersection B=2. So, the number of elements in AintersectionB is 1. So n(a intersection B)=1

The Easiest Number Theory Problem

The answer is 1.

7 solutions

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